An Idealized Model of Matrix Storage and the Tidal Response of Coastal Aquifers

Sandy Hardian Susanto Herho , Dasapta Erwin Irawan, Iwan Pramesti Anwar, Rusmawan Suwarman, Deny Juanda Puradimaja

Tides entering a coastal aquifer weaken and lag the sea as they travel inland, and classical theory requires the two rates to be equal. Field records often show the amplitude decaying faster than the phase lag grows, which is usually attributed to geometry or leakage. We examine a third mechanism, the exchange of water between a conduit network and the matrix blocks it surrounds, and ask when this exchange makes the aquifer behave as a fractional medium in time. The study is purely theoretical. For each tidal constituent, the measured decay and lag are exactly equivalent to a complex storage capacity at that frequency, so a single constituent cannot separate memory from leakage. Passive storage exchange and leakage can never make the lag rate exceed the decay rate, and diffusive exchange with blocks of any sizes cannot reduce their ratio below a fixed bound close to two fifths. A power law distribution of block sizes produces a fractional medium over a band of frequencies, with an order between one half and one set by the exponent of the distribution. In the nonlinear unconfined aquifer, the period mean of the squared head is conserved with or without memory, and the mean rise of the water table depends on the decay rate alone. For a karstic reference aquifer, one month of four tidal constituents reliably separates memory from leakage even when the matrix stores a fifth as much water
as the conduits. All closed forms are verified numerically.